There are numerous preprocessing methods to handle approximate distance queries, and one of them is constructing spanners [1]}, [2]}. On a connected graph \(G\) , a spanner is a spanning subgraph with integer parameters \(\alpha \ge 1\)  and \(\beta \ge 0\) , such that for all vertices \(v_1\)  and \(v_2\) ,
\(d^{\prime }(v_1,v_2) \le \alpha \cdot d(v_1,v_2) + \beta .\) 
